Question

The zeroes of the quadratic polynomial are √2 and -√2, then the quadratic polynomial is ?

Answer 1

Zeroes are root2, - root2

Sum of zeroes = root2 - root2 = 0

Product of zeroes = root2 × (-root2) = - 2

Required polynomial = x^2 - (sum of zeroes)x + Product of zeroes

= x^2 - (0)x + (-2)

= x^2 - 2

Answer 2

Hola bro!!!!

Formula for making quadratic polynomial is ....

$p(x) = {x}^{2} - ( \alpha + \beta ) \times x + \alpha \beta$


$\alpha = \sqrt{2} \\ \\ \beta = - \sqrt{2}$
$\alpha + \beta = \sqrt{2} + ( - \sqrt{2} ) = \sqrt{2} - \sqrt{2} = 0 \\ \\ \alpha \beta = \sqrt{2} \times ( - \sqrt{2} ) = - 2$

So your answer is ....

$p( x) = {x}^{2} - ( 0) \times x + (- 2) \\ \\ = {x}^{2} - 2$


Hope it helps